“A brief study of Unique factorization domain in Integral Domain”

Srivastav, Dr. Amrish Kumar

doi:https://doi.org/10.55041/ijcope.v2i5.561

Volume 02, Issue 05

Published on: May 2026

“A BRIEF STUDY OF UNIQUE FACTORIZATION DOMAIN IN INTEGRAL DOMAIN”

Dr. Amrish Kumar Srivastav

Department of Mathematics Araria College Araria

DOI:https://doi.org/10.55041/ijcope.v2i5.561

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Abstract

Unique Factorization Domains (UFDs) are integral domains where every non zero non unit element can be factored into irreducible elements in a manner that is unique, considering order and units. This idea extends the Fundamental Theorem of Arithmetic from integers to more abstract algebraic structures. This paper offers a comprehensive examination of UFDs within integral domains, covering definitions, equivalent characterizations, significant theorems, examples, counter examples and their connections to principal ideal domains and Euclidean domains. Additionally, applications in algebraic number theory and polynomial theory are explored.

Keywords: Integral domains, Euclidean, ideal domains

How to Cite this Paper

Srivastav, A. K. (2026). “A brief study of Unique factorization domain in Integral Domain”. International Journal of Creative and Open Research in Engineering and Management, <i>02</i>(05). https://doi.org/10.55041/ijcope.v2i5.561

Srivastav, Amrish. "“A brief study of Unique factorization domain in Integral Domain”." International Journal of Creative and Open Research in Engineering and Management, vol. 02, no. 05, 2026, pp. . doi:https://doi.org/10.55041/ijcope.v2i5.561.

Srivastav, Amrish. "“A brief study of Unique factorization domain in Integral Domain”." International Journal of Creative and Open Research in Engineering and Management 02, no. 05 (2026). https://doi.org/https://doi.org/10.55041/ijcope.v2i5.561.

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References

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•Published on: May 19 2026

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